Show that all the diagonal elements of a skew symmetric matrix ar… - Vidyadip

Question

Show that all the diagonal elements of a skew symmetric matrix are zero.

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Answer

Let $\text{A} = [\text{a}_{\text{ij}}]_{\text{n}\times\text{n}} $ be skew symmetric matrix.
A is skew symmetric
$\therefore \text{A = -A}' $
$\Rightarrow \text{a}_{\text{ij}} = \text{-a}_{\text{ji}} \text{ }\forall \text{ i, j}$
For diagonal elements i = j,
$\Rightarrow \text{2a}_{\text{ii}} = 0$
$\Rightarrow \text{a}_{\text{ii}} = 0 \Rightarrow$ diagonal elements are zero.

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